The 139La(n,γ) cross section: Key for the onset of the s...

PHYSICAL REVIEW C 75, 035807 (2007)

The 139La(n, γ ) cross section: Key for the onset of the s-process

R. Terlizzi,19 U. Abbondanno,20 G. Aerts,7 H. Alvarez,34 F. Alvarez-Velarde,30 S. Andriamonje,7 J. Andrzejewski,25

P. Assimakopoulos,16 L. Audouin,12 G. Badurek,1 P. Baumann,10 F. Becvar,6 E. Berthoumieux,7 M. Calviani,18 F. Calvino,33

D. Cano-Ott,30 R. Capote,3,35 A. Carrillo de Albornoz,26 P. Cennini,36 V. Chepel,27 E. Chiaveri,36 N. Colonna,19 G. Cortes,32

A. Couture,40 J. Cox,40 M. Dahlfors,36 S. David,9 I. Dillmann,12 R. Dolfini,23 C. Domingo-Pardo,31 W. Dridi,7 I. Duran,34

C. Eleftheriadis,13 M. Embid-Segura,30 L. Ferrant,9 A. Ferrari,36 R. Ferreira-Marques,27 L. Fitzpatrick,36 H. Frais-Koelbl,4

K. Fujii,20 W. Furman,29 R. Gallino,22 I. Goncalves,27 E. Gonzalez-Romero,30 A. Goverdovski,28 F. Gramegna,18

E. Griesmayer,4 C. Guerrero,31 F. Gunsing,7 B. Haas,8 R. Haight,38 M. Heil,12 A. Herrera-Martinez,36 M. Igashira,24 S. Isaev,9

E. Jericha,1 Y. Kadi,36 F. Kappeler,12 D. Karamanis,16 D. Karadimos,16 M. Kerveno,10 V. Ketlerov,28,36 P. Koehler,39

V. Konovalov,29,36 E. Kossionides,15 M. Krticka,6 C. Lamboudis,13 H. Leeb,1 A. Lindote,27 I. Lopes,27 M. Lozano,35 S. Lukic,10

J. Marganiec,25 L. Marques,26 S. Marrone,19,* C. Massimi,21 P. Mastinu,18 A. Mengoni,3,36 P. M. Milazzo,20 C. Moreau,20

M. Mosconi,12 F. Neves,27 H. Oberhummer,1 S. O’Brien,40 J. Pancin,7 C. Papachristodoulou,16 C. Papadopoulos,14

C. Paradela,34 N. Patronis,16 A. Pavlik,2 P. Pavlopoulos,11 L. Perrot,7 M. Pignatari,22 R. Plag,12 A. Plompen,5 A. Plukis,7

A. Poch,32 C. Pretel,32 J. Quesada,35 T. Rauscher,37 R. Reifarth,38 M. Rosetti,17 C. Rubbia,23 G. Rudolf,10 P. Rullhusen,5

J. Salgado,26 L. Sarchiapone,36 I. Savvidis,13 C. Stephan,9 G. Tagliente,19 J. L. Tain,31 L. Tassan-Got,9 L. Tavora,26

G. Vannini,21 P. Vaz,27 A. Ventura,17 D. Villamarin,30 M. C. Vincente,30 V. Vlachoudis,36 R. Vlastou,14 F. Voss,12

S. Walter,12 H. Wendler,36 M. Wiescher,40 and K. Wisshak12

(n TOF Collaboration)1Atominstitut der Osterreichischen Universitaten, Technische Universitat Wien, Vienna, Austria

2Institut fur Isotopenforschung und Kernphysik, Universitat Wien, Vienna, Austria3International Atomic Energy Agency, NAPC-Nuclear Data Section, Vienna, Austria

4Fachhochschule Wiener Neustadt, Wiener Neustadt, Austria5CEC-JRC-IRMM, Geel, Belgium

6Charles University, Prague, Czech Republic7CEA/Saclay-DSM, Gif-sur-Yvette, France

8Centre National de la Recherche Scientifique/IN2P3-CENBG, Bordeaux, France9Centre National de la Recherche Scientifique/IN2P3-IPN, Orsay, France

10Centre National de la Recherche Scientifique/IN2P3-IReS, Strasbourg, France11Pole Universitaire Leonard de Vinci, Paris La Defense, France

12Forschungszentrum Karlsruhe GmbH (FZK), Institut fur Kernphysik, Karlsruhe, Germany13Aristotle University of Thessaloniki, Thessaloniki, Greece

14National Technical University of Athens, Greece15NCSR, Athens, Greece

16University of Ioannina, Ioannina, Greece17ENEA, Bologna, Italy

18Istituto Nazionale di Fisica Nucleare(INFN), Laboratori Nazionali di Legnaro, Legnaro, Italy19Dipartimento di Fisica and Istituto Nazionale di Fisica Nucleare, Bari, Italy

20Istituto Nazionale di Fisica Nucleare, Trieste, Italy21Dipartimento di Fisica, Universita di Bologna and Sezione INFN di Bologna, Bologna, Italy

22Dipartimento di Fisica, Universita di Torino and Sezione INFN di Torino, Torino, Italy23Universita degli Studi Pavia, Pavia, Italy

24Tokyo Institute of Technology, Tokyo, Japan25University of Lodz, Lodz, Poland

26Instituto Tecnologico e Nuclear(ITN), Lisbon, Portugal27LIP-Coimbra & Departamento de Fisica da Universidade de Coimbra, Coimbra, Portugal

28Institute of Physics and Power Engineering, Obninsk, Russia29Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Dubna, Russia30Centro de Investigaciones Energeticas Medioambientales y Technologicas, Madrid, Spain

31Istituto de Fısica Corpuscolar, CSIC-Universidad de Valencia, Valencia, Spain32Universitat Politecnica de Catalunya, Barcelona, Spain

33Universidad Politecnica de Madrid, Madrid, Spain34Universidade de Santiago de Compostela, Spain

35Universidad de Sevilla, Seville, Spain36CERN, Geneva, Switzerland

37Department of Physics and Astronomy, University of Basel, Basel, Switzerland38Los Alamos National Laboratory, Los Alamos, New Mexico, USA

39Oak Ridge National Laboratory, Physics Division, Oak Ridge, Tennessee, USA

0556-2813/2007/75(3)/035807(15) 035807-1 ©2007 The American Physical Society

R. TERLIZZI et al. PHYSICAL REVIEW C 75, 035807 (2007)

40University of Notre Dame, Notre Dame, Indiana, USA(Received 24 October 2006; published 26 March 2007)

The nuclear resonance parameters and the capture cross section of the neutron magic isotope 139La havebeen measured relative to 197Au in the energy range of 0.6 eV to 9 keV at the neutron time-of-flight (n TOF)facility at CERN. We describe the experimental apparatus and the data analysis procedures, which concernedmainly the efficiency correction by means of the pulse height weighting function technique and the determinationof different background components. We extracted the resonance parameters and the main nuclear quantitiessuch as the resonance integral RI = 10.8 ± 1.0 b, the average γ widths for s and p waves 〈�γ 〉l=0 = 50.7 ±5.4 meV and 〈�γ 〉l=1 = 33.6 ± 6.9 meV, the nuclear level densities 〈D〉l=0 = 252 ± 22 eV and 〈D〉l=1 <

250 eV, and the neutron strength functions S0 = (0.82 ± 0.05) × 10−4 and S1 = (0.55 ± 0.04) × 10−4. Theseresults represent a significant improvement over previous data. The deduced Maxwellian-averaged capture crosssections are important for the interpretation of the most recent spectroscopic observations in low-metallicity stars.

DOI: 10.1103/PhysRevC.75.035807 PACS number(s): 25.40.Lw, 26.20.+f, 27.60.+j, 97.10.Cv

I. INTRODUCTION

Isotopes with closed neutron shells such as 139La (N = 82)are of special importance in nuclear physics. Their nuclearstructure is characterized by low level densities and a smallstrength of the reaction channels, resulting in a low totalneutron cross section that is dominated by the elastic channel.The cross sections and the nuclear structure of these nucleiprovide useful information for fundamental nuclear physicsstudies (microscopic calculations of many-body systems [1])as well as for applications in nuclear astrophysics and nucleartechnology. Concerning the latter aspect, 139La is an abundantfission fragment (5% fission yield [2]) and is widely usedfor neutron dosimetry in nuclear power plants because of therelatively long half-life (t1/2 = 1.678 d) of 140La [3].

Lanthanum assumes a relevant role in nuclear astrophysics.It is copiously produced by the main component of theslow neutron capture process (s-process) but receives also asizable contribution from the rapid neutron capture process(r-process). The dominant isotope 139La (99.91% in solar La)belongs to the second s-process peak shaped by the N =82 nuclei from Ba to Nd and is particularly well suited formonitoring the s-process abundances from Ba up to Pb. More-over, it is relatively easy to observe in stellar spectra, becausetransition probabilities and hyperfine structure constants ofseveral lanthanum levels have been accurately measured [4].Together with updated stellar atmosphere models and the useof high-resolution spectra, the lanthanum abundance can bereliably determined in stars of different metallicities. Theseanalyses depend sensitively on the Maxwellian-averaged neu-tron capture cross section (MACS) at the typical temperaturesof the astrophysical site of the main s-process.

Unlike lanthanum, the close-by element europium is cur-rently chosen as the best monitor of the r-process. Europium iscomposed of two isotopes, 151Eu and 153Eu with solar isotopicabundances of 47.8% and 52.2%, respectively. The s-processcontribution to solar europium is small (∼6%), because bothisotopes have very high neutron capture cross sections. The

*Corresponding author, address: via Orabona 4, 70125 Bari, Italy.Tel. +390805442511, e-mail: [email protected]

spectroscopic determination of the europium abundance isbased on a selected number of lines with accurately measuredhyperfine structure constants [5]. Accordingly, europium isa good marker of the r-process abundance distribution. Inparticular, correlated observations of lanthanum and europiumabundances at various metallicities can provide an effectivemonitor of the chemical evolution in the Galaxy.

Time-of-flight (TOF) measurements of the 139La(n, γ )cross section have been performed at Oak Ridge [6] andJAERI [7], and a transmission measurement was reported fromthe Columbia University synchrotron [8]. Recently, severalactivation measurements [9–11] have provided evidence forsubstantial systematic uncertainties in the previous TOFdata. The serious astrophysical consequences resulting fromdiscrepancies of up to 40% among the experimental datamotivated a new capture cross section measurement at theinnovative neutron time-of-flight (n TOF) facility at CERN.The main features of the n TOF installation such as the longflight path, the extremely high instantaneous neutron flux, andthe low background conditions together with an optimizeddetection setup provided an ideal basis for accurate TOFmeasurements in a wide energy range, both for radioactivesamples and for isotopes with very low capture cross sections,such as 139La.

In the following, the main characteristics of the facilityand the experiment are described in Sec. II, the data analysisprocedures in Sec. III, and the resulting resonance parametersin the resolved region from 0.6 eV up to 9 keV in Sec. IV. Theimplications for fundamental nuclear physics and for nuclearastrophysics are discussed in Sec. V.

II. EXPERIMENTAL APPARATUS

The main characteristics of the facilities, experimentalapparatus, and data analysis procedures have been publishedin detail [12–15]. Therefore, we furnish here, together witha general description, only the specific features related to thelanthanum measurement.

A. The n TOF facility

At n TOF, neutrons are generated via spallation by the20 GeV/c protons from the CERN Proton Synchrotron (PS)

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http://dx.doi.org/10.1103/PhysRevC.75.035807

THE 139La( n, γ ) CROSS SECTION: KEY FOR . . . PHYSICAL REVIEW C 75, 035807 (2007)

TABLE I. Main characteristics of the n_TOF facility.

Parameter Comment

Proton beam 20 GeV/c momentum, 7 ns (rms) pulse widthRepetition rate 0.4 Hz (average)Intensity 7 × 1012 protons/pulse

Neutron beam 300 neutrons/protonEnergy range from 0.6 eV to 250 MeV (set by

the performance of the data acquisition system)One magnet, two collimators, and heavy Fe

and concrete shielding for background reductionNeutron filters for background definition∼105 neutrons/pulse/energy decade at

185 m distance from the spallation targetNeutron energy resolution �E/E = 10−3

at 30 keV

accelerator complex impinging onto a massive target of naturallead. The measuring station is located 187.5 m from thespallation target, inside the tunnel that houses the evacuatedneutron flight path. Because of the prolific neutron productionprovided by spallation reactions and the very intense beamof 7 × 1012 protons/pulse, the instantaneous neutron flux atn TOF is more than two orders of magnitude higher thanat other facilities. Backgrounds due to charged particles andγ rays originating from the spallation target are efficientlyreduced by several meters of concrete and iron shieldings, asweeping magnet, and a combination of two collimators. Thecollimators serve to shape the neutron beam and to shieldscattered neutrons from the target. The signal generated by theremaining fraction of ultrarelativistic particles (the so-calledγ flash) can be used for defining the start of the time-of-flightmeasurement. For the capture cross section measurements atn TOF, an aperture 19 mm in diameter is used for the secondcollimator in front of the experimental area. This results in aneutron beam with an approximately Gaussian profile of 11.75mm full width at half maximum at the sample position. Themain features of the n TOF facility are summarized in TableI; for more technical details, see Refs. [12–14].

B. Detectors and data acquisition

The prompt capture γ rays were detected with twoC6D6 liquid scintillation detectors with an active volume of∼1000 cm3 [16]. The scintillator is contained in a thin-walledcarbon fiber cell, which is directly coupled to an EMI 9823QKA phototube without any further structural material aroundin order to minimize the sensitivity to sample scatteredneutrons. The detectors are positioned 9.8 cm upstream ofthe sample with the front being about 3 cm from the beam axisas indicated by the schematic sketch of the setup in Fig. 1.The samples were mounted on a remotely controlled samplechanger made from carbon fiber, which is directly integratedin the vacuum of the neutron beamline. Up to five samplescan be mounted on the internal sample ladder for periodicbackground and reference measurements (see below).

The setup for the capture measurements is complementedby the silicon flux monitor (SiMon). The flux monitor consists

SampleNeutron Beam

C6D6

C6D6

-ray

FIG. 1. Schematic sketch of n TOF beamline illustrating therelative positions of sample and detectors.

of a thin 6Li deposit on a thin Mylar foil surrounded by aset of four silicon detectors outside the neutron beam [17]for recording the tritons and α particles from the 6Li(n, α)3Hreaction. This device is used for monitoring the neutron fluxand to provide the normalization of the count rates measuredwith the different samples.

Because of the high instantaneous neutron flux, severalevents are generally recorded for a single neutron bunch. Toavoid pileup and dead-time problems, a data acquisition systembased on high-frequency flash analog-to-digital converters(FADC) has been developed at n TOF [18]. The FADCmodules can be operated with sampling rates up to 1 billionper second and are equipped with 8 MBytes of buffer memoryfor each channel. The raw data are recorded signal by signalfor detailed off-line analysis, which allows one to extract therequired information on timing, charge, amplitude, and particleidentification.

C. Samples

The characteristics of the samples are summarized inTable II together with the number of protons used for themeasurement of each sample. In addition to the La under

TABLE II. Sample characteristics and relative numberof protons used in lanthanum measurement.

Sample Diameter(mm)

Mass(g)

Number ofprotons (×1017)

natLa+Al can 20 1.943 1.353Al can (empty) 20 0.357 0.646natC 20 3.933 0.423208Pb 20 4.941 0.551197Au 20 2.873 0.757Total 3.730

035807-3


investigation, a gold reference sample as well as a natural Cand a 208Pb sample were used in the present measurement. TheLa sample consisted of a natural metal foil (99.91% 139La and0.09% 138La) enclosed in a low-mass aluminum canning. TheAu reference sample was included because the gold capturecross section is known with good accuracy, particularly in theregion around the resonance at 4.9 eV and between 10 and200 keV [19]. This sample is, therefore, used for neutronflux normalization [20]. The C and 208Pb samples servedto determine the background components related to samplescattered neutrons and in-beam γ rays.

III. DATA ANALYSIS

The main steps in data analysis consist of the efficiencycorrection by means of the pulse height weighting technique(PHWT), followed by the determination and subtraction ofthe different background components and by the absolutenormalization of the neutron flux. These aspects and minoradditional corrections for dead time, self-shielding, and mul-tiple scattering are discussed in this section.

A. Pulse height weighting technique

Because of their low efficiency, the C6D6 detectors normallydetect only a single γ ray of the capture cascade. Theprobability of detecting a capture event depends, therefore,on the multiplicity of the cascade as well as on the energyof the emitted γ rays, because of the intrinsic efficiencyof the liquid scintillator. With the PHWT, [21] the detectorresponse R(En,ED), with En the neutron energy and ED

the energy deposited in the scintillator, is modified in sucha way that the detection efficiency becomes independent ofthe cascade properties, but is completely determined by theneutron separation energy [15]. For obtaining the weightingfunction required for this correction, WF(ED), a set of responsefunctions is calculated for each sample by detailed MonteCarlo simulations using the GEANT-3 [22] and MCNP [23]software packages. In these simulations, the geometry and ma-terials of the experimental setup were carefully implemented,and the points of origin of the photons were modeled accordingto the Gaussian neutron beam profile. The weighting functionswere then defined by fitting the simulated response functionswith a polynomial of degree four [see Eq. (3) in Ref. [15]].

The efficiency correction has to be corrected for coinci-dence events and for dead time. Coincident detection of twoγ rays has to be corrected because the PHWT is based onthe assumption that only one γ ray per capture cascade isrecorded. In general, this condition is ensured by the lowoverall efficiency of the liquid scintillator. In the case of 139La,it is also supported by the low average cascade multiplicitiesand the low binding energy of 5.71 MeV. The probabilityfor coincidences can be determined by the probability forcoincidences between the two detectors, which was 2.1%for the adopted coincidence window of 20 ns. Since thecorresponding correction for the Au reference sample wasfound to be 2.3%, the true correction on the yield for La wasless than ∼1% with a relative uncertainty of 0.1%.

In principle, the dead time of the n TOF data acquisitionsystem is negligible, but events can be reliably separatedonly if they are separated by more than 20 ns. This causesa virtual dead time, which has been estimated by means ofthe “paralyzable model” [24] approximation. In the 139Lameasurement, this correction was negligible, except on topof the largest resonances (i.e., at 72 eV), where it reached only∼0.5%.

With these corrections, the capture yield YRaw can beexpressed by means of the PHWT [21] as

Ecasc

∫�(E′

n)YRaw(E′n)dE′

n

=10 MeV∑

ED = 0.2 MeV

R(En,ED)WF(ED), (1)

where �(En) is the total neutron fluence seen by the sample,and Ecasc is the total capture energy converted to the laboratoryframe. This raw yield has to be further corrected for the differ-ent background components as well as for other effects suchas Doppler broadening, self-shielding, multiple scattering, andneutron energy resolution. The raw capture yields of natLa,carbon, and lead samples are shown in Fig. 2.

B. Background

As reported in Ref. [25], the capture measurements atn TOF are mainly affected by the “ambient” backgroundand by the sample-related contributions (in-beam γ raysand scattered neutrons). The ambient background is mostlygenerated by the effect of the sample canning and by particles

NEUTRON ENERGY (eV)1 10 210 310 410 510 610

CA

PT

UR

E Y

IEL

D

-510

-410

-310

-210

-110LANTHANUMTOTAL BACKGROUND

NEUTRON ENERGY (eV)1 10 210 310 410 510 610

CA

PT

UR

E Y

IEL

D

-510

-410

-310

-210CAl CAN

Pb

FIG. 2. (Color online) Top: Capture yield of La sample and totalbackground. Bottom: Individual background components. In the keVregion, the effect of in-beam γ rays measured with the Pb sampledominates over the component due to sample scattered neutrons,whereas the contribution of the Al can is always comparably small.

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TABLE III. Normalization factors for correc-tion of backgrounds due to in-beam γ rays (kγ )and to neutrons scattered by the sample (kn).

Factor natLa 197Au natC 208Pb

kγ 0.335 0.665 – 1kn 0.100 – 1 –

produced in the spallation target or in the collimators, whichsomehow reach the experimental area and produce signalsin the capture setup. This component, which was estimatedby means of an empty aluminum container identical to thatenclosing the lanthanum sample, is relatively low with respectto the lanthanum yield (Fig. 2).

A quantitative estimate of the background due to in-beamγ rays was obtained for each sample by scaling the contributionmeasured with a 208Pb sample by means of detailed MonteCarlo simulations. These simulations were performed fornatLa, 197Au, and 208Pb (with and without the Al can) withthe GEANT-3 package by using a detailed software modelof the experimental apparatus. The respective γ -ray spectrawere obtained by FLUKA simulations of the spallation andmoderation process [26]. The 208Pb sample is particularlysuited for this correction because it is very sensitive to γ rays(high atomic number) and has a very low capture cross section(doubly magic). The contribution of in-beam γ rays is isolatedin the 208Pb spectra by subtracting the ambient backgroundmeasured with the Al can, as indicated in Eq. (2). Since the208Pb sample was not encapsulated, the subtracted contributionof the Al can was estimated with Monte Carlo simulations andtaken into account by rescaling kγ by approximately 2%.

The background from neutrons scattered by the sample andcaptured in or near the detectors was estimated by means of thecarbon sample, because carbon is transparent to in-beam γ raysand has a cross section that is dominated by the elastic channel.The scattering background is determined by subtracting thespectrum of the Al can (Fig. 2) and by rescaling the resultingyield with the normalization factor kn, which is determined bythe ratio between the scattering effect of the natLa sample andof the carbon sample (Table III). This correction was found tobe a few percent below 100 eV but negligible at higher neutronenergies.

As illustrated in Fig. 2, the lanthanum yield is clearlyabove the total background up to 9 keV. Below 1 keV, thebackground is determined by the ambient component, whereasthe contribution from in-beam γ rays dominates in the upperpart of the spectrum. According to the previous considerations,

the background subtracted capture yield is

YBS(En) = Ysample(En) − YAl-can(En) − kγ [YPb(En)

−YAl-can(En)], (2)

where Ysample is the raw capture yield measured for thesample under study (La or Au), and YAl-can and YPb are theyields measured with the Al and 208Pb samples, respectively.The second term represents the environmental background,while the third term takes into account the in-beam γ -raycomponent as described previously. All capture yields areconsistently calculated using the same set of the weightingfunctions. The normalization for the total neutron fluence isobtained by the means of the SiMon neutron monitor. Othercorrections concerning the neutron flux and scattered neutronsare described below.

C. Neutron flux determination

Different detectors and techniques are employed at n TOFto determine the total neutron flux. The most importantand complete results are obtained with the calibrated fissionchamber from PTB Braunschweig, with the SiMon, and withthe analysis of standard resonances in the capture reactions of197Au, Ag, and 56Fe. The combination of these measurementsyields the experimental neutron flux with an accuracy ofbetter than 2% [12–14]. However, since the sample diameteris smaller than the neutron beam profile, only a fraction ofthis beam interacts with the capture samples. To estimate thisfraction, the total flux is normalized according to the standard197Au(n, γ ) cross section, which is well known in the keVregion and is considered standard for the resonance at 4.9 eV.

In the resolved resonance region from 1 to 100 eV, the fluxfraction is calculated by fitting the main 197Au resonances withthe R-matrix code SAMMY [27]. In the unresolved region, thenormalization factor is evaluated by dividing, bin per bin, thegold cross section measured at n TOF with the gold referencecross section [19]. The respective fractions of the beam seen bythe samples, Cflux, are listed in Table IV for different neutronenergies together with the results from FLUKA simulations.These values agree with beam profile measurements performedwith a Micromegas [20] detector. All experimental data andsimulations confirm that the beam fraction Cflux increaseswith neutron energy and must therefore be considered inthe determination of the capture yield. Where available, theexperimental values of Cflux are used in the analysis (e.g., in theregions 1–100 eV and 10–100 keV). In the remaining energyregions, the results from the simulations were normalized tothe experimental values.

TABLE IV. Fraction of neutron flux seen by the sample extracted from gold data and from FLUKA

simulations (adopted values).

Energy range 1–10 eV 10–100 eV 0.1–1 keV 1–10 keV 10–100 keV

Cflux (exp.) 0.480 ± 0.010 0.482 ± 0.010 – – 0.504 ± 0.021Cflux (sim.) 0.480 0.483 0.488 0.493 0.500

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TABLE V. Resonance parameters (ER, �γ , and g�n), radiativecapture strengths (g�n�γ /�tot), and orbital angular momentumassignment (l) for the n+139La system. Fixed values in the SAMMY fitsare marked by an asterisk. The g�n values are adopted from Hackenet al. [8], while average γ widths 〈�γ 〉l are used when �n � �γ .

ER (eV) �γ (meV) g�n (meV) g�n�γ /�tot

(meV)l

0.758 ± 10−3 40.11 ± 1.94 5.6 × 10−5 ±5 × 10−6

5.6 × 10−5 1

72.30 ± 0.05 75.64 ± 2.21 11.76 ± 0.53 8.68 0249.1 ± 0.1 33.6∗ 0.167±9×10−3 0.17 1339.8 ± 0.5 33.6∗ 0.162±9×10−3 0.16 1617.8 ± 1.2 36.35 ± 1.58 13.35 ± 0.75 8.08 0703.8 ± 1.9 15.29 ± 0.93 6.20 ± 0.19 4.49 1876.4 ± 2.6 25.45 ± 1.24 12.79 ± 0.64 6.75 0906.2 ± 3.1 18.57 ± 0.68 4.49 ± 0.19 3.65 1963.6 ± 4.1 29.48 ± 1.53 8.64 ± 0.45 5.17 01181 ± 4 91.62 ± 2.73 923∗ 38.41 01209 ± 5 19.73 ± 1.55 8.10 ± 0.98 4.68 11257 ± 5 26.13 ± 3.50 15.82 ± 0.33 6.64 11429 ± 6 33.6∗ 0.071±6×10−3 0.07 11433 ± 6 33.6∗ 2.15 ± 0.12 1.93 11639 ± 7 27.31 ± 2.01 43.9 ± 6.5 9.39 01652 ± 7 14.84 ± 2.93 32.3 ± 5.9 5.41 01828 ± 10 7.99 ± 1.05 5.25 ± 0.13 3.24 11918 ± 10 28.23 ± 2.71 4.63 ± 0.24 3.36 11973 ± 10 18.52 ± 2.75 2.21 ± 0.30 1.60 12119 ± 12 61.40 ± 4.70 1702∗ 26.44 02155 ± 12 39.75 ± 2.75 480∗ 21.36 02178 ± 12 48.39 ± 2.97 5.80 ± 0.35 4.55 12383 ± 14 51.10 ± 2.85 29.8 ± 2.1 12.77 02472 ± 14 62.53 ± 4.16 507∗ 32.89 02667 ± 15 38.98 ± 2.66 20.91 ± 1.62 9.40 02859 ± 16 27.66 ± 3.55 197.8∗ 11.40 02968 ± 16 26.32 ± 1.04 15.45 ± 0.33 9.95 12994 ± 16 31.32 ± 2.85 5751∗ 17.56 03011 ± 16 10.80 ± 0.70 11.76 ± 0.41 5.81 13292 ± 18 51.41 ± 2.40 1032∗ 22.01 03429 ± 19 30.15 ± 2.58 0.90 ± 0.09 0.84 13461 ± 19 39.16 ± 2.49 6.61 ± 0.35 4.77 13481 ± 19 52.31 ± 2.80 7197∗ 29.30 03554 ± 20 9.07 ± 3.59 10.81 ± 1.12 3.46 13735 ± 21 87.38 ± 3.77 91.48∗ 26.96 03754 ± 21 57.91 ± 3.60 2571∗ 32.17 03991 ± 23 30.72 ± 1.95 61.3 ± 8.1 21.31 14120 ± 23 72.79 ± 4.59 54.9 ± 7.2 32.13 14309 ± 24 61.69 ± 4.25 21.94 ± 3.41 10.26 14361 ± 25 35.88 ± 4.20 2509∗ 15.6034 04616 ± 27 52.06 ± 3.52 31.3 ± 3.1 13.18 14658 ± 27 41.23 ± 4.10 1172∗ 22.89 04740 ± 27 38.06 ± 3.75 43.7 ± 3.5 12.05 14823 ± 29 31.94 ± 3.39 76.10∗ 11.80 05167 ± 30 25.00 ± 1.75 11.58 ± 4.30 8.06 15191 ± 30 37.77 ± 1.70 57.2 ± 5.1 15.49 15287 ± 30 33.00 ± 2.60 44.2 ± 3.5 10.88 15357 ± 31 26.10 ± 4.01 599∗ 11.20 05533 ± 33 24.71 ± 2.63 126.4∗ 12.52 05838 ± 35 67.06 ± 2.78 603.1∗ 35.50 05860 ± 35 80.48 ± 4.64 88.2 ± 3.6 43.41 1

TABLE V. (Continued.)

ER (eV) �γ (meV) g�n (meV) g�n�γ /�tot

(meV)l

5879 ± 35 8.58 ± 1.25 68.9 ± 3.5 8.05 05937 ± 36 20.21 ± 1.43 327.5 ± 12.2 20.15 15983 ± 36 38.11 ± 2.61 286.1∗ 19.93 06036 ± 36 38.89 ± 2.73 24.91 ± 1.82 8.17 16148 ± 37 19.98 ± 1.95 16.82 ± 1.63 6.73 16343 ± 38 61.84 ± 4.10 64.1 ± 4.3 14.85 16467 ± 38 38.90 ± 2.64 2089∗ 16.88 06600 ± 39 59.88 ± 4.08 753∗ 25.31 06766 ± 41 46.13 ± 3.25 50.4 ± 3.5 11.21 16974 ± 42 98.84 ± 6.61 601∗ 40.34 07004 ± 42 21.75 ± 2.94 441 ± 38 9.31 07060 ± 43 31.13 ± 1.62 44.9 ± 3.4 12.60 17107 ± 43 11.47 ± 4.48 35.0 ± 3.1 4.39 17144 ± 44 53.29 ± 3.92 1300∗ 29.30 07271 ± 45 54.46 ± 4.09 24.13 ± 1.98 11.99 17458 ± 47 101.8 ± 5.36 1002∗ 42.63 07561 ± 47 33.02 ± 2.60 130.3∗ 16.26 07632 ± 49 30.72 ± 1.65 24.03 ± 2.53 8.62 17783 ± 50 58.52 ± 5.41 35.1 ± 3.7 14.80 18000 ± 52 52.06 ± 14.12 1126 ± 143 28.51 08042 ± 52 130.4 ± 9.4 1299∗ 54.68 08142 ± 53 17.29 ± 1.44 135.2∗ 7.16 18400 ± 55 45.87 ± 3.81 228.6∗ 18.45 08534 ± 56 95.33 ± 7.71 2491∗ 41.02 08655 ± 56 43.48 ± 3.55 372.5∗ 18.10 08707 ± 57 43.49 ± 3.63 121.5∗ 33.48 18910 ± 58 21.18 ± 1.79 56.3 ± 3.5 9.83 18970 ± 58 56.87 ± 4.71 3682∗ 24.71 0

D. Other corrections

The determination of the resonance parameters requiresthat several minor effects have to be taken into account. Theseare the Doppler broadening of the resonance widths due to thethermal motion, the energy resolution of the neutron beam, theisotopic contamination of the sample, and the self-shieldingand multiple scattering effects in the sample.

All these corrections are included in R-matrix fits withSAMMY, which is used to extract the resonance parameterslisted in Table V. The Doppler broadening is implementedaccording to the free-gas model with a temperature T =300 K and dominates over other sources of broadeningbelow 1 keV neutron energy. The resolution function of then TOF neutron beam [28] becomes important above 1 keVneutron energy, where it describes the increasingly asymmetricresonance shape.

The very small isotopic impurity of 138La contributesto the low-energy part of the spectrum, as illustrated inFig. 3. It is taken into account in the resonance fit by thecorresponding resonance parameters from the JENDL-3.3nuclear data library.

The self-shielding and multiple scattering corrections arean integral part of the standard SAMMY implementation.Considering the low total cross section of the lanthanum, asizable modification of the resonance parameters is produced

035807-6


NEUTRON ENERGY (eV)

10 20 30 40 50 60 70 80 90 100

CA

PT

UR

E Y

IEL

D

-410

-310

-210

-110

FIG. 3. Background subtracted capture yield of the La samplefitted with SAMMY. According to Mughabghab et al. [29], the smallresonances at 3, 20, 68, and 89 eV are due to the minute 138La impurityof 0.09%.

only for the largest resonances, where the probability ofelastic scattering is high. Generally, these effects modify theshape of the resonances by depressing the resonance peaksand overestimating the tails toward higher energy. Thesecorrections affect the capture yield by a few percent withuncertainties of less than 1%.

IV. RESULTS

A. Resonance parameters

The capture cross section of 139La is expressed in terms ofR-matrix resonance parameters calculated in the Reich-Mooreapproximation with the code SAMMY [27]. The fit of theresonances, see Figs. 3 and 4, is performed in different waysin order to check the reliability of the extracted parameters. Ingeneral, the three resonance parameters ER,�γ , and �n are leftfree to vary, while, according to the discussion in the previoussection, the normalization factor is kept fixed. The mainsteps of the fitting procedure consist in the extraction of theresonance parameters from the background-subtracted captureyields. The spin assignment of each level is carefully checkedby comparing the fits obtained with different assignmentsindicated in the ENDF/B-VI.8, JEFF-3.1, and JENDL-3.3libraries [30]. For many levels, especially when �n � �γ ,the best fit is found by adopting the transmission value as theneutron width, whereas in the few cases with �γ � �n, theγ width is fixed to the average value (Table V). When the �n areleft free to vary, our neutron widths are roughly consistent with

NEUTRON ENERGY (keV)6.8 7 7.2 7.4 7.6 7.8 8 8.2

CA

PT

UR

E Y

IEL

D

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0

FIG. 4. SAMMY fit of the La capture yield in the keV region.

the results of the transmission measurement [8]. The remainingdifferences might be attributed to the fact that several p-wavelevels (in this work, but especially in Hacken et al. [8]) aremissing and that the neutron width does not always dominatethe total width of the resonance but fluctuates following aPorter-Thomas distribution. In some cases, the capture channelmay therefore provide a sizable contribution to the total crosssection, while in other cases, this contribution is negligible.This feature can also be inferred from the trend of the s- andp-wave neutron strength functions shown in Figs. 5 and 6.

The capture yields YCapture and the neutron capture crosssection σγ are related by the equation

YCapture(En) = (1 − exp[−NAtomsσtot(En)])σγ (En)

σtot(En), (3)

where σtot is the total neutron cross section and NAtoms is thenumber of atoms per barn. However, this expression does notconsider several corrections already described in this worksuch as the neutron flux normalization, multiple scattering,Doppler broadening, and neutron beam resolution. Some ofthese effects are included in the following relation, assuminga thin sample (NAtomsσγ � 1):

YExperimental(En) = NAtomsCflux(En)

CMS(En)σγ (En), (4)

where CMS takes into account the self-shielding and multiplescattering corrections, and Cflux is the normalization factor asestimated in the previous section. Doppler broadening and theresolution function of the neutron beam are not included inEq. (4) because they entail complicated relations. However,

NEUTRON ENERGY (keV)

0 1 2 3 4 5 6 7 8 9

# O

F L

EV

EL

S B

EL

OW

NE

UT

RO

N E

NE

RG

Y

0

5

10

15

20

25

30

35

40


0 1 2 3 4 5 6 7 80

100

200

300

400

500

600

700

9

(meV

) 0

nΓg

∑

FIG. 5. Cumulative number of levels (top) and cumulative sum ofneutron widths (bottom) of the s-wave resonances. Dashed line fittedto the data indicates that the sequence of the s-wave levels seems tobe complete.

035807-7



0 1 2 3 4 5 6 7 8 9# O

F L

EV

EL

S B

EL

OW

NE

UT

RO

N E

NE

RG

Y

0

5

10

15

20

25

30

35

40


0 1 2 3 4 5 6 7 8 90

100

200

300

400

500

600

(meV

) 1 nΓ

g∑

FIG. 6. Same as Fig. 5, but for p-wave resonances. The fit to thecumulative number of the levels is limited to the region between 0and 2.5 keV, where the p-wave level sequence seems to be complete.The fit of the cumulative sum of the neutron widths includes the entireenergy range.

both effects are included in the SAMMY fit together with thecontribution of the potential scattering, which is calculatedtheoretically using a radius R′ = 5.1 fm [29]. This full analysiswas checked by determining the resonance parameters fromfits of the experimental data prior to background subtraction.Generally, the parameters obtained in this way are withinuncertainties consistent with those derived by the background-subtracted capture yield.

In our full analysis, three new resonances were identified,and improved parameters were obtained for the previouslyknown resonances. The final results extracted from thebackground-subtracted spectra are listed in Table V. As shownin Sec. IV B, the fitting procedure allowed us to evaluatethe statistical and systematic uncertainties of the lanthanumcapture cross section in a coherent way. The results of somefits in the resolved resonance energy region up to 9 keV areillustrated in Figs. 3 and 4. According to the level assignmentindicated in the Ref. [29], some neutron capture resonances ofthe 138La impurity (0.09%) can be seen in Fig. 3 at 3, 20, 67,and 89 eV neutron energy.

Up to 9 keV, all levels reported by Hacken et al. [8]and Musgrove et al. [6] could be identified. The three newresonances are p waves at neutron energies of 6.036, 6.766,and 7.783 keV. In general, the orbital angular momentumassignments by Hacken et al. on the basis of the Bayesstatistical analysis are confirmed, while most of the additionalresonances detected by Musgrove et al. are p waves. Up to2 keV, the resonances energies ER are in good agreementwith previous results, but differences appear for resonances

between 6 and 8 keV. It seems that the accuracy of theresonance energies has been overestimated by Hacken et al.,who took only the flight-path contribution into account but didnot include the neutron beam resolution (see Ref. [31]).

The comparison of the capture strengths (g�n�γ /�tot) de-rived from the n TOF data with previous results indicates thatour capture strength is on average about 10% lower than thatreported by Nakajima et al. [7] and a few percent lower thanthose of Musgrove et al. [6]. A possible explanation for thesesystematic differences can be due to a more reliable evaluationof the PHWT, an accurate treatment of the corrections forself-shielding, multiple scattering, and the effect of neutronenergy resolution, and the use of the well-tested R-matrixcode SAMMY. Finally, systematic uncertainties are significantlyreduced by the improved n TOF setup, which exhibits muchlower neutron sensitivity by the use of low-mass carbon fibercells for the liquid scintillator detectors. In addition, the use ofFADCs provides an efficient way for n/γ discrimination [32],and the extremely low repetition rate of one neutron burstevery 2.4 s avoids pulse overlap and provides a low neutroninduced background. It is important to note that these featuresprovide possible explanations for the systematic differencesbetween our results and previous data, but that there is noclear experimental evidence for the real causes. In particular,there seems to be no correlation between �n and �γ for thewhole set of resonances.

To compute the MACS and the resonance integral, thepresent data have to be complemented to cover the range up to1 MeV in neutron energy. The comparison with the evaluatedcross sections from the JENDL, ENDF, and JEF nuclear datalibraries [30] shows that the n TOF results agree best withJENDL in terms of orbital angular momentum assignmentsand of general resonance properties. The better agreementcould be due to the fact that the JENDL evaluation takes allprevious measurements [6–8] into account. Nevertheless, thecapture cross sections measured at n TOF are lower than theJENDL data, by about 10% in the first part of the neutronenergy spectrum (<1 keV) and by 3% on average between 5and 9 keV.

As illustrated in the next section, the main nuclear inputfor determining the lanthanum abundance in stellar modelcalculations are the MACS for a range of stellar temperaturesbetween kT = 5 and 100 keV, which are obtained by foldingthe capture cross section with a Maxwell-Boltzmann typeneutron spectrum in a wide energy range (100 eV to 500keV). Since the n TOF results cover only part of this spectrum,only the partial contribution to MACS can be accuratelydetermined, as indicated by P-MACS in Table VI. In viewof the remaining differences between the n TOF data andJENDL-3.3, the accurate experimental result of the MACSmeasured at kT = 25 keV with the activation method byO’Brien et al. [10] at Forschungszentrum Karlsruhe (FZK) hasbeen considered. The MACS calculated at kT = 25 keV usingthe n TOF data and the JENDL cross section is 5% higherthan the FZK MACS. To reproduce the measured values ofn TOF and FZK, the JENDL cross section is renormalized withrespect to the n TOF data between 9 and 15 keV (by a factorof 0.97) and at higher energies with respect to the FZK MACS(by a factor of 0.95). The MACS uncertainties are calculated

035807-8


TABLE VI. Maxwellian-averaged (n, γ ) cross sec-tions. Values in column 2 correspond to the partial infor-mation from the present measurement (1 eV to 9 keV).The third column contains the MACS averaged over thefull thermal spectrum after complementing the measureddata by the normalized JENDL-3.3 data between 9 and500 keV. MACS at 25 keV (in parentheses) is adoptedfrom Ref. [10] and was used for normalization.

kT (keV) P-MACS (mb) MACS (mb)

5 83.5 ± 4.6 106.9 ± 5.38 45.9 ± 3.0 74.8 ± 4.1

10 33.2 ± 2.5 63.2 ± 3.912.5 23.4 ± 1.9 53.9 ± 3.815 17.4 ± 1.5 48.1 ± 3.817.5 13.4 ± 1.1 43.8 ± 3.720 10.7 ± 0.9 40.3 ± 3.325 7.2 ± 0.6 (35.7)30 5.2 ± 0.4 32.4 ± 3.135 3.9 ± 0.3 29.8 ± 3.040 3.0 ± 0.3 27.7 ± 2.845 2.4 ± 0.2 25.3 ± 2.550 2.0 ± 0.2 23.6 ± 2.460 1.4 ± 0.1 22.0 ± 2.270 1.1 ± 0.1 19.9 ± 2.085 0.7 ± 0.06 17.4 ± 1.7

100 0.5 ± 0.04 15.2 ± 1.5

propagating the errors of the capture cross section used inthe folding procedure. According to the previous discussion,the systematic uncertainty on the evaluated nuclear data isestimated to be around 10%.

A confirmation that this procedure is reasonable and theexperimental data are accurate comes from recent activationmeasurements at FZK [10,11]. Unlike the case of a promptcapture γ -ray measurement, the activation technique is notaffected by background from scattered neutrons and is,therefore, particularly well suited for the measurement oflow capture cross sections. The MACS evaluated by O’Brienet al. [10] at a thermal energy of kT = 30 keV (31.6 ±0.8 mb) is 37% lower than the MACS obtained by Musgroveet al. [6] (50 ± 5 mb). The most recent result for the MACS,obtained with the activation method by Winckler et al. [11] atkT = 5 keV (113.7±4.9 mb), is within the quoted uncertaintyconsistent with the n TOF value of 106.9 ± 5.3 mb.

Using the same approach, the resonance integral, definedas

RI =∫ 1 MeV

0.5 eVσγ (En)/EndEn, (5)

is calculated to be 10.8 ± 1.0 b, which is 8.5% lower thanthe 11.8 ± 0.8 b given in Ref. [29] but only 4.5% lowerthan a previous measurement (11.2 ± 0.5 b) [33]. This resultis consistent with the observation that the capture strengthshave been found to be smaller than those from previousmeasurements [6,7] especially at low energy. The smalldifference between the experimental RI [33] and the n TOF

TABLE VII. Uncertainties of the lanthanum (n, γ ) measurement.Statistical error represents the major contribution to the totaluncertainty. Statistical uncertainties become larger at higher neutronenergy because of the lower counting rate, see text for details.

Source Statistical WF Flux Minor effects Total

Uncertainty (%) 4–8 1.5 2 0.5 4.7–8.5

value can be ascribed to the uncertainty of the thermal capturecross section, which is not measured in this work.

B. Uncertainty analysis

In the resolved resonance region, the total uncertaintiesrelated to the resonance parameters are derived from theR-matrix fit performed with the SAMMY code. The uncer-tainties (1σ ) of the parameters are listed in Table V. Thecontribution of each component to the total uncertainty isdiscussed in the following, and a summary of the error balanceis reported in Table VII.

1. Statistical

Due to the low capture cross section of lanthanum, thestatistical error represents the most important contribution tothe final uncertainty. The statistical errors from the PHWT

analysis are not simply given by the number of events in agiven neutron energy bin, but also have to be calculated bypropagating the errors in the definition of the yields in Eq. (1)[34]. The total background is increasing with neutron energyand becomes comparable to the cross section at 9 keV, thusadding also a significant contribution. For the chosen energybinning, the sum of the contributions from the gold sample (seenext paragraphs), the La sample, and the background rangesfrom 4% to 8%.

2. Weighting function

The overall uncertainty due to the PHWT has beendetermined by the comparison of the capture yields extractedwith different sets of weighting functions (WF). In fact, theweighting functions obtained with different codes or usingdifferent thresholds or a different polynomial order (third orfourth) in the least squares method lead to differences ofup to 3% in the extracted yield. These discrepancies are re-duced to less than 1.5%, if the cross section is measured relativeto a reference sample (i.e., Au), provided that the weightingfunctions are consistently calculated for both samples. In thiscase, the systematic effects (geometrical details, tracking ofthe photons, etc.) affect both samples similarly and cancel outto a large part. The remaining 1.5% uncertainty is a realisticvalue for the present measurement, because the uncertainty ofthis method was determined in Ref. [15] to be less than 2%from a complete analysis of the standard resonances in Au,Ag, and Fe.

035807-9


3. Neutron flux

This systematic uncertainty is related to the shape ofthe absolute neutron flux that has been determined by thecombination of different measurements [12–14] with anuncertainty of less than 2%. An additional contribution tothis uncertainty is associated with the determination of thefraction of the beam seen by the sample, because the samplediameter was smaller than the beam size. As described before,the gold standard cross section was used to estimate the fractionCflux with a total uncertainty (statistical and systematic) ofless than 4% (see Table IV). The combined fitting procedure,together with the detailed simulations, leads to an improvedaccuracy for these fractions of 2%. It is therefore reasonableto adopt a value of 2% for the systematic uncertainty of theflux normalization, as indicated in Table VII.

4. Minor effects

The number of atoms in each sample is very well deter-mined by the mass measurement listed in Table II. Also, the138La impurity is well known by the natural composition of thesample. Therefore, the associated error is much less than 0.1%and was neglected. Uncertainties due to Doppler broadening,beam resolution, and self-shielding and multiple scatteringcorrections are estimated according to the total, elastic, andcapture cross sections calculated by SAMMY. These correctionsand other minor effects contribute at most a few percent to thecapture yield, with average uncertainties of about 0.5%.

The total uncertainties of the resonance parameters areestimated on average to be about 6.5% (see Tables V and VII).The PHWT and flux determination constitute the main sys-tematic contributions to those errors, as reported in Table VII,while the uncertainties of the minor corrections are practicallynegligible except in the largest resonances. As a consequenceof the low capture cross section of 139La, the largest uncer-tainty of this measurement is therefore due to the statisticalcontribution.

V. IMPLICATIONS

A. Nuclear structure

The accurate resonance analysis presented for the neutronmagic isotope 139La is of interest for several reasons. The leveldensities and the relative strength functions of the compoundnucleus 140La can be derived for the different assignments ofthe orbital angular momentum. Since 139La has spin 7/2, thecompound nucleus has two possible total angular momentumvalues J = 3 and 4 for the 39 s-wave resonances, and fourvalues J = 2, 3, 4, and 5 for the 40 p-wave levels. Theorbital angular momentum is deduced from the resonancefits, which take the previously known neutron widths intoaccount. For the s- and p-wave sets of levels, the averagespacing 〈D〉 calculated from the maximum likelihood fit ofa Wigner distribution, the average γ widths 〈�γ 〉, and theneutron strength function S obtained by fitting the cumulativesum of the reduced neutron widths are summarized in

TABLE VIII. Nuclear quantities of the n + 139La compoundsystem derived from the observed s- and p-wave resonancesbetween 0.6 eV and 9 keV.

s wave p wave

〈�γ 〉l=0 = 50.7 ± 5.4 meV 〈�γ 〉l=1 = 33.6 ± 6.9 meV〈D〉l=0 = 252 ± 22 eV 〈D〉l=1 < 250 eVS0 = (0.82 ± 0.05) × 10−4 S1 = (0.55 ± 0.04) × 10−4

�3,Exp = 0.57 ± 0.10 –�3DM = 0.72 ± 0.22 –�3GOE = 0.60+0.16

−0.22 –

Table VIII. The reduced neutron widths for s waves are

�0n = �n

(1.0 eV

ER

)1/2

, (6)

and for p waves,

�1n = 1 + (ka)2

(ka)2 �0n, (7)

where k is the neutron wave number in the laboratory frame anda is the nuclear hard-sphere radius calculated according to theformula a = 0.8 + 1.23A1/3 fm [30]. The cumulative numberof levels and the cumulative sum of the reduced neutron widthsfor the s- and p-wave levels are shown in Figs. 5 and 6.All fits are performed for the entire neutron energy range(0.6 eV to 9 keV) except for the cumulative number of p-waveresonances. In this case, the energy range was restricted toenergies below 2.5 keV because the sequence of the p-wavelevels seems complete only up to this energy. Figures 5 and6 also provide important information concerning the nuclearstructure of the compound nucleus. While the sequence ofs-wave resonances seems to be complete up to 9 keV, thereduced neutron widths oscillate more than predicted by thePorter-Thomas (P-T) distribution, especially between 3 and4 keV. This observation was already reported by Hackenet al. [8] for 139La, 140Ce, and 141Pr as a hint of undetectedintermediate structures in these neutron magic nuclei. On thecontrary, the good linearity of the cumulative sum of theneutron widths in Fig. 6 suggests that the strongest p-waveresonances are almost all detected and that the missing levelshave very low capture strength.

To check the completeness of the level sequence, as wellas the reliability of the orbital angular momentum assignment,statistical �3 tests [35] are performed for the s- and p-waveensembles, and the number of missing levels is estimated viathe P-T distribution of the reduced neutron widths g�l

n forl = 0 and 1. In particular, the theoretical �3 value is initiallycalculated according to the Dyson-Mehta (�3,DM) theory; seeEq. (81) in Ref. [35]. To have a further confirmation of thisresult and to assess more certain conclusions, we simulatedthe behavior of the �3 statistic according to the Gaussianorthogonal ensemble (GOE) matrices theory. Two sets ofconsecutive eigenvalues were extracted from two independentsamples of 80 000 GOE matrices of dimension 300 × 300randomly generated. From 39 consecutive eigenvalues ofeach matrix, the corresponding �3 value was calculated.

035807-10


Finally, after having summed the two samples, the averagevalue (�3,GOE) and the relative confidence region of the �3

distribution were determined. According to those results, thestatistical significance, i.e., the probability that �3 � �3,Exp,is 54%, while it is smaller if a number of missing resonancesis assumed. Note also that �3,DM and �3,GOE were calculatedfor a level spacing ratio DJ=3/DJ=4 = 1.22, although theseresults are quite insensitive with respect to this ratio. Theexperimental and theoretical �3 values are compared inTable VIII for the total number of s waves. Although thenumber of levels of this ensemble is relatively poor (39), thoseresults (�3,Exp,�3,DM,�3,GOE, and statistical significance) arecompatible with the assumption that the set of s-wave levels iscomplete. For the p-wave resonances, the standard deviationof theoretical �3 is much larger than the experimental valuebecause of the four possible J assignments. This featureinduces large fluctuations in the cumulative number of p-wavelevels and makes the relative statistical analysis ineffective.

Integration of the P-T distribution for a single levelpopulation provides the number of total levels, which can becalculated for s and p waves according to

N (x) = Nl[1 − erf(√

x/2)], (8)

where l = 0 or 1, x = g�ln/〈g�l

n〉 , and Nl is the totalnumber of expected levels. The maximum likelihood fits ofboth distributions according to Eq. (8) are illustrated in Fig. 7.The number of estimated s-wave levels is N0 = 39 ± 3,in perfect agreement with the experimental result, whereasN1 = 54 ± 5 indicates that we are missing 25% of thep levels. However, the estimate for the p-wave resonancesis only indicative since we were not able to determine J .In fact, the analysis of the p-wave ensemble was performedaccording to the P-T single-channel distribution, but includingall possible J values. The correct approach [36,37] would havebeen to treat the J = 3 and 4 states by means of a two-channelP-T distribution (p1/2 and p3/2 neutron interactions), whilethe J = 2 and 5 levels could be described by a single-channel P-T distribution (p3/2). Nevertheless, the conclusionsof this analysis support the previous observations derived fromFigs. 5 and 6 and from the �3 tests.

B. Nuclear astrophysics

Lanthanum plays an important role in the determinationof the s-process abundances of the heavy elements. Togetherwith the other isotopes of the second s peak around the magicneutron number N = 82, lanthanum acts as a bottleneckbetween the abundant light n-capture elements Sr, Y, and Zrbelonging to the first s peak at magic number N = 50 and theheavy elements from Sm up to Pb and Bi. Lanthanum is also agood marker in the interpretation of stellar spectra, because itis practically monoisotopic and its absorption spectra containseveral lines with accurately measured transition probabilitiesand hyperfine structure constants [4]. The remaining problem,partly solved by this work, has been the lack of reliableMACS values for the low-temperature phase of s-processnucleosynthesis around kT = 8 keV.

⟩n 0Γ g⟨ / n

0Γ gx =

-310 -210 -110 1 10

xN

UM

BE

R O

F L

EV

EL

S A

BO

VE

05

101520253035404550

⟩n 1 Γ g⟨ / n

1Γ gx =

-310 -210 -110 1 10x

NU

MB

ER

OF

LE

VE

LS

AB

OV

E

0

10

20

30

40

50

60

FIG. 7. Cumulated number of levels with values larger than x fors waves (top) and p waves (bottom). Dotted curves indicate the fitsvia Eq. (8), confirming that the s-wave ensemble seems completewhile p waves are clearly missing at low values of x.

Once the s-process abundance is accurately determinedwith respect to solar lanthanum, the r-process contributionis completely fixed by the residual, Nr = N�–Ns . Thisdecomposition is crucial for the understanding of chemicallyunevolved stars in the Galactic halo, which exhibit heavy ele-ment patterns that are essentially of r-process origin producedby short-lived massive progenitor stars [38,39]. Exceptions arethe extrinsic asymptotic giant branch (AGB) stars [40], whichinclude the majority of C-rich stars [41,42], the s-processrich stars [43–45], the Pb-rich stars [46], and other peculiarstars, such as the r-process-rich ones [47]. All these starshave quite different abundance distributions compared to theunevolved halo stars because of the mass transfer that occurs ina binary system or the pollution caused by a nearby supernova.Therefore these stars must be excluded from the sample ofunevolved halo stars. Note, however, that the literature datashown in Figs. 8 and 9 contain a few chemically peculiarstars, which have been added to the selected sample starsbecause of their unusually high [La/Eu]1 ratio of >0.2 dex,the typical range predicted for the s-enhanced extrinsic AGBstars. A typical [La/Eu]s ∼ 0.9 dex is indeed predicted by thes-process, and that observed for an extrinsic AGB star dependson the degree of pollution.

1The spectroscopic notation indicates that: [A/B] = log10(A/B) −log10(A/B)� where A and B are elemental abundances. The symbol� indicates that the abundance is referred to the solar value.

035807-11


[Fe/H]

[Fe/H]

-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

[La/

Fe]

-1

-0.5

0

0.5

1

1.5

-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

[Eu

/Fe]

-1

-0.5

0

0.5

1

1.5

2

FIG. 8. (Color online) Observed spectroscopic ratios of La (top)and Eu (bottom) with respect to Fe as a function of metallicity.(References used are denoted by symbols: black triangles [48], redstars [49], blue crosses [50], green squares [51], blue circles [52], andblue diamonds [53]). A typical error bar is shown in the lower rightcorner. Stars observed by different authors are connected by dashedlines.

Previously, barium was the preferred indicator for the heavys-process elements in stellar spectra, because the capturecross sections of the related isotopes are all well known [55].Barium has a relatively large solar abundance among the heavyelements (4.43 relative to Si = 106 in the solar system) [56]and the most part of it (∼80%) is synthesized by the s-process.Apart from the rare 130,132Ba nuclei (which represent only0.2% of solar Ba), barium is composed of five isotopes, from134Ba to 138Ba. The two s-only isotopes 134,136Ba contribute10% to solar barium, while the neutron magic 138Ba, mostly ofs-process origin, contributes 71.7%. Notice that the odd isotope137Ba (11.2% of solar Ba) is also mainly of s-process origin[54]. From the spectroscopic point of view, however, bariumpresents several disadvantages. Barium exhibits only a fewspectral lines, one is often saturated (4554 A) and the othersare difficult to detect. In addition, the hyperfine splitting by thevarious isotopes contributes noticeably to a spread of stronglines. These features lead to relatively large uncertainties inthe spectroscopy of barium and a corresponding scatter in theabundance determinations. Eventually, these uncertainties inthe spectroscopic observations put into question the use ofbarium for monitoring the s-process contributions in stars. Incontrast, lanthanum is not affected by such ambiguities and istherefore considered as the more reliable s-process indicator.

Initially, the decomposition of the s-process abundanceand the corresponding r-process residuals was based on theclassical s-process approach [57], where three components

(main, weak, and strong) were invoked for describing the solars-process distribution [58]. This phenomenological model hasmeanwhile led to inconsistencies in describing the s abun-dances of the Nd isotopes and of the branching in the reactionpath at 141Ce, 142Pr, 147Nd, 148Pm and 151Sm [59], and was,therefore, essentially abandoned. The main s component inthe solar system is associated with nucleosynthesis processesin low-mass stars (� 8M�) while evolving along the AGBand suffering recurrent thermal instabilities (thermal pulses,TPs) in the He shell (for a review, see Busso, Gallino, andWasserburg [60]). After each TP, freshly synthesized 12C ands-process elements from between the He- and H-burning zone(the He intershell) are mixed to the surface by third dredge-upepisodes. Along the AGB phase, the star progressively losesits entire envelope by very efficient stellar winds, in this wayreturning s-enriched material to the interstellar medium.

The major neutron source in AGB stars is provided bythe 13C(α, n)16O reaction, which operates at the top of theHe intershell in the so-called 13C pocket. This phase ischaracterized by low neutron densities (∼107 cm−3) and lowtemperatures (kT ≈ 8 keV) and operates between TPs underradiative conditions for periods of about 104 yr [61,62]. Asecond source of neutrons is provided by the 22Ne(α, n)25Mgreaction, which is marginally activated at high temperatures(kT ≈ 20–25 keV) during TPs for a much shorter timeinterval of 5 to10 yr. Though high peak neutron densities up to1011 cm−3 are reached, the time-integrated neutron flux islimited to about 5% of the total neutron budget. During a TP,the whole He-intershell region becomes convective. According

[Fe/H]-3 -2.5 -2 -1.5 -1 -0.5 0

[La/

Eu

]

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

et al.O’Brien

This Work

et al.Arlandini et al.Winckler

FIG. 9. (Color online) Spectroscopic ratio of La with respect toEu as a function of metallicity. Symbols are the same as in Fig. 8.The r-process ratios calculated according to the thermal-pulse-AGBmodel are indicated by horizontal lines, illustrating the result of thiswork compared with the results of O’Brien et al. [10] and Winckleret al. [11]. Note that the older data used by Arlandini et al. [54]led to [La/Eu] ratios, that are higher than the observed values atvery low metallicity. An indicative and average error bar is shownon the lower right. The shaded area represents the total error of thespectroscopic ratio, which is induced mainly by the uncertainties ofthe solar elemental abundances. Stars having high [La/Eu] values(0.2–0.4) represent the s-process-rich stars and require a differenttreatment, see text for details.

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to this scenario, the solar main component is the result of allprevious generations of AGB stars in the Galaxy. As a matterof fact, the buildup of the s elements is not a unique processbut depends on the metallicity and initial stellar mass as wellas on the strength of the 13C pocket and on the mass loss rate.

With the present MACS of 139La, the TP-AGB model of themain component yields an s-process contribution of 74 ± 3%of the solar lanthanum abundance, very close to the valuesobtained by O’Brien et al. (76.9%) [10] and by Winckleret al. [11] (70.0%), consistently higher than that reported byArlandini et al. [54] (64.2%) on the basis of the previousMACS (see also Fig. 9). Our MACS, at kT = 30 keV, isidentical to that of O’Brien et al., but 6% lower at 5 keVcompared to the result of Winckler et al. The small differencesin the inferred s abundance of 139La are, in fact, due to theMACS at low temperatures, because La is predominantlyproduced in the 13C pocket. While the minor neutron exposureby the 22Ne neutron source plays an important role forbranching isotopes like 151Sm [63], which has a high MACS, ithas almost no impact on the final abundance of neutron magicisotopes like 139La.

The improved understanding of the s-process production oflanthanum is important for Galactic chemical evolution. Thes-process is not of primary origin, because the necessary Feseed does not result directly from hydrogen and helium burningin the same star. Consequently, the s-process abundancedistribution depends on the stellar metallicity, initial mass, andstrength of the carbon pocket [60]. Moreover, low-mass AGBstars have a very long lifetime of several Gyr. Therefore, themain component cannot contribute to the chemical enrichmentof the early universe. In fact, the heavy s elements appearonly at metallicities [Fe/H] > −2 [64–66]. Besides the maincomponent, also the strong s component is the outcome ofthe s-process nucleosynthesis operating in AGB stars, asdiscussed in the references. In fact, recent studies [60,67,68]have identified in the low metallicity ([Fe/H] < −1.5) andlow-mass AGB stars the astrophysical origin of the synthesis ofthe strong s component. This production mechanism accountsfor almost 50% of solar 208Pb and 20% of solar 209Bi. Onlythe weak s-process, which occurs in the shorter-lived massivestars (>8M�), contributes the s nuclei up to A ≈ 90 alreadyat earlier times. This component is synthesized partly inthe helium-burning cores of massive stars and partly in thesubsequent convective carbon-burning shell.

Unlike the s-process, the r-process is believed to be ofprimary origin, in particular for the heavy elements beyondBa. Possible astrophysical sites are type II supernovae andneutron star mergers, which are principally suited to producingthe extremely high neutron densities required to describe ther-process abundance distribution, but there are open questionsremaining for both scenarios (for a review, see Truran et al.[38]). Since it is occurring in massive stars (>8M�), whichhave short lifetimes of less than 0.1 Gyr, the r-processdominated the production of heavy elements in the earlyuniverse. This is confirmed by the observation of metal-poorhalo stars, which exhibit clear r-process patterns. The analysisof TP-AGB stars has shown that the s-process contributions toeuropium is very low ( ∼6%) and not affected by the branchingof the s path in this mass region [65]. From the spectroscopic

point of view, the europium abundance in stars is generallylow (0.095 relative to Si = 106 in the solar system) [56],but the Eu lines are well resolved, and the respective hyperfineconstants are accurately measured [5]. Therefore, the europiumabundances can be reliably established, and even isotopicratios have been determined by hyperfine splitting analyses ofthe spectral lines [69]. Because of these features, europium rep-resents a good marker of the r-process abundance distribution.

In principle, the increase of the metal abundances is corre-lated with the age of the Galaxy, thus providing a sort of cosmo-chronometer. Metal-poor stars are particularly important inthis respect, because they represent the oldest observablestellar population. According to the previous discussions, thes-process can be characterized by lanthanum, and the r-processby europium, and the metallicity can be used as a chronometer.Hence, the combination of these quantities permits one tofollow the chemical evolution of the Galaxy. In Figs. 8 and9, the spectroscopic ratios [La/Fe], [Eu/Fe], and [La/Eu] areshown as a function of metallicity [Fe/H] for 227 stars in ametallicity range between 0 and −3. Most of these data arefrom Burris et al. [48] and Simmerer et al. [49], complementedby the r-process enhanced stars measured by McWilliam et al.[50], Johnson and Bolte [51], Honda et al. [52], and Barklemet al. [53]. The [element/Fe] ratio at low metallicity exhibitslarge variations of ±1 dex (Fig. 8) because the iron productionat low metallicity cannot be considered an effective chronome-ter [70,71] or because of inhomogeneities of the interstellarmedium [39,72–74]. The large dispersion of the heavy ele-ments in halo stars is also attributed to incomplete mixing ofthe interstellar medium in the first epochs of the Galaxy.

The results obtained in this work are most relevant withrespect to the spectroscopic ratio [La/Eu] plotted in Fig. 9.Since the main s-process starts to contribute to the heavy ele-ment abundances for metallicities [Fe/H] � −1.5, the earlierlanthanum abundance should correspond to the much smallerr-process value, whereas the r-process element europium isproduced at solar proportions. At low metallicities, the [La/Eu]ratio should, therefore, correspond to the r-process value of−0.56 ± 0.07, as indicated in Fig. 9 by the dashed-dotted line.The expected increase of the [La/Eu] at metallicities > −1.5due to the later s contributions is clearly confirmed by theobservational data.

The rise of the heavy element abundance from a purer-process level due to the progressive enrichment by s-processelements emerged a few years ago thanks to observational[50,75,76] and theoretical [63,71] studies. While these argu-ments first used the observed barium abundances [48,77–79],they now rely more on lanthanum instead [49]. These studieshave to be further pursued to clarify a number of open questionsresulting from uncertainties in the observational data, in thenuclear aspects, and in the stellar models. For example, it isinteresting to note that Johnson and Bolte [48] and Barklemet al. [49] do not find any rise of the [La/Eu] ratio in the entirerange −3< [Fe/H] < −1.5 over the r-process value (Fig. 4 inRef. [51] and Fig. 20 in Ref. [53]).

In conclusion, the TOF measurement of the 139La(n, γ )cross section has led improved MACS calculations at thelow thermal energies, which are crucial for the determinationof the s-process abundance of lanthanum. Nevertheless, the

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TABLE IX. Selected stars from Figs. 8 and 9 showing differencesof more than 0.2 dex in the spectroscopic ratios reported by differentauthors. Discrepant values are indicated by bold numbers.

Star Ref. [Fe/H] [La/Fe] [Eu/Fe] [La/Eu]

HD-2796 [48] −2.23 −0.22 −0.06 −0.16[50] −2.52 −0.48 0.12 −0.60

HD-6268 [50] −2.59 −0.03 0.68 −0.71[52] −2.63 0.21 0.52 −0.31

HD-29574 [48] −1.81 0.38 0.76 −0.38[51] −1.84 −0.18 0.20 −0.38

HD-74462 [49] −1.51 0.15 0.59 −0.45[48] −1.56 −0.06 0.32 −0.38

HD-110184 [49] −2.50 −0.16 0.26 −0.42[48] −2.56 0.11 0.45 −0.34

HD-115444 [51] −2.71 0.26 0.83 0.57[49] −3.16 0.17 0.57 0.40

HD-122956 [49] −1.69 0.02 0.37 −0.36[48] −1.78 0.04 0.55 −0.51

HD-128279 [49] −2.13 −0.24 0.03 −0.28[51] −2.40 −0.30 0.10 −0.40

HD-165169 [51] −2.24 −0.15 0.41 −0.39[48] −2.32 0.19 0.58 −0.49

HD-171496 [49] −0.61 −0.04 0.22 −0.26[48] −0.91 −0.47 −0.15 −0.32

HD-186478 [52] −2.61 0.07 0.61 −0.53[51] −2.42 0.01 0.54 −0.54

HD-204543 [49] −1.72 −0.01 0.21 −0.22[48] −1.84 0.27 0.46 −0.19

HD-206739 [48] −1.58 −0.17 0.35 −0.52[49] −1.61 0.10 0.46 −0.36

HD-232078 [49] −1.40 −0.17 0.15 −0.32[48] −1.54 0.12 0.40 −0.28

uncertainties in the astronomical observations both for thestars’ abundances and for the solar abundances still remainlarge. In fact, as illustrated in Figs. 8 and 9, the error onthe spectroscopic ratios for each star is on average 0.2 dex.Moreover, in several cases the results of different observationalgroups disagree with each other for both the metallicity valuesand the heavy elements abundance estimates (see Table IX).For clarity, in Figs. 8 and 9, the error bars of the abundances ofthe single stars are not drawn, whereas single stars observed

by different authors are connected with a dashed line. Table IXlists also the stars whose abundances show striking variations(�0.2 dex) between different observers. In addition, the shadedarea in Fig. 9 represents the total error induced mainly bythe solar abundance uncertainties (∼15% corresponding to±0.072 dex) estimated according to the data published inRef. [56]. We must remark that a different compilation [80]of solar abundances dedicates a special treatment to the rareearth elements and estimates a lower uncertainty (∼ 3%corresponding to ±0.021 dex). It is evident that this kindof uncertainty represents the major problem in the accuratedetermination of the r-process spectroscopic ratios. Thissituation should greatly benefit from the ongoing coordinatedefforts in high-resolution spectroscopy.

VI. CONCLUSIONS

This paper reports the 139La(n, γ ) cross section measuredat n TOF. The capture cross section is given in terms ofresonance parameters in a large energy range from 0.6 eVup to 9 keV. These results show sizable differences withrespect to the previous experimental data and allow one toextract the related nuclear quantities with improved accuracy.The results are important to the nuclear structure aspects ofneutron magic isotopes, nuclear technology, and particularly,the nucleosynthesis history of the Galaxy. The new capturecross sections have led to substantially improved Maxwellian-averaged cross sections at the comparably low thermal energyof kT = 8 keV characteristic of the dominant s-processneutron source. This improvement contributed to the analysisof the La and Eu abundances over a wide range of stellarmetallicity, which opens new vistas on the chemical evolutionof the Galaxy.

ACKNOWLEDGMENTS

S. M. wishes to acknowledge J. J. Cowan for usefuldiscussions concerning the elemental spectroscopic ratios.This work has been partly supported by the EC within theframework of the n TOF-ND-ADS project (nuclear data foraccelerator systems, Contract FIKW-CT-2000-00107) and bythe funding agencies of the participating institutes.

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